We analyze the information content of density profiles for an ultracold Bose gas of atoms and extract resolution limits for observables contained in these images. Our starting point is density correlations that we compute within the Bogoliubov approximation, taking into account quantum and thermal fluctuations beyond mean-field theory. This provides an approximate way to construct the joint counting statistics of atoms in an array of pixels covering the gas. We derive the Fisher information of an image and the associated Cramer-Rao sensitivity bound for measuring observables contained in the image. We elaborate on our recent study on position measurements of a dark soliton [Negretti et al., Phys. Rev. A 77, 043606 (2008)] where a sensitivity scaling with the atomic density as n^{-3/4} was found. We discuss here a wider class of soliton solutions and present a detailed analysis of the Bogoliubov excitations and the gapless (Goldstone) excitation modes. These fluctuations around the mean field contribute to the noise in the image, and we show how they can actually improve the ability to locate the position of the soliton.
Bose statistics imply a substantial enhancement at small angles for light scattering off a cold, Bose gas. The enhancement increases dramatically at the Bose-Einstein temperature. This phenomenon could be utilized to eliminate almost entirely the heating of the gas by a weak probe light beam.
The phase transitions in Bose gases at constant volume and constant pressure are considered. New results for the chemical potential, the effective Landau-Ginzburg free energy and the equation of state of the Bose condensate in ideal Bose gases with a general form of the energy spectrum are presented. Unresolved problems are discussed.
Dynamical instabilities due to spin-mixing collisions in a $^{87}$Rb F=1 spinor Bose-Einstein condensate are used as an amplifier of quantum spin fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in quantitative agreement with mean-field calculations. We quantify the microscopic spin fluctuations of the initially paramagnetic condensate by applying this amplifier and measuring the resulting macroscopic magnetization. The magnitude of these fluctuations is consistent with predictions of a beyond-mean-field theory. The spinor-condensate-based spin amplifier is thus shown…
By extending Einstein's separation of wave and particle parts of the second order thermal fluctuation to encompass "generalized fluctuations" in any Bose field, P. E. Gordon has proposed alternative definitions for nth order coherence and nth order coherent states. The main point of this paper is to explore some of the physical insights to be gained by extending dualism to higher orders. Recent experiments have examined aspects of the coherence of Bose-Einstein condensates. It has been argued that the condensate state is coherent to (at least) second or third order, but the coherence propertie…
The fluctuations of the atom number between a Bose-Einstein condensate and the surrounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the predicted peak fluctuations is observed when using a microcanonical with respect to a can…
For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground state occupation becomes macroscopic, the condensate number fluctuations remain micrscopic. However, this is the only significant aspect in which the grand canonical description differs from canonical or microcanonical in the thermodynamic limit. General arguments and estimates including some vanishingly small quantities are compared to explicit, fixed-number calculations for 10^2 to 10^6 particles.
The problem of particle fluctuations in arbitrary nonuniform systems with Bose-Einstein condensate is considered. This includes the case of trapped Bose atoms. It is shown that the correct description of particle fluctuations for any nonuniform system of interacting atoms always results in thermodynamically normal fluctuations.
We report in situ measurements of density fluctuations in a quasi one dimensional Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected bunching for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the…
Based on the canonical ensemble, we suggested the simple scheme for taking into account Gaussian fluctuations in a finite system of ideal boson gas. Within framework of scheme we investigated the influence of fluctuations on the particle distribution in Bose -gas for two cases - with taking into account the number of particles in the ground state and without this assumption. The temperature and fluctuation parameter dependences of the modified Bose- Einstein distribution have been determined. Also the dependence of the condensation temperature on the fluctuation distribution parameter has been…
Even at zero temperature, there exist phase fluctuations associated with an array of Bose-Einstein condensates confined in a one-dimensional optical lattice. We demonstrate a method to measure the phase fluctuations based on the Fourier spectrum of the atomic density for a condensate released from the optical lattice. The phase variance is extracted from the relative intensities of different peaks in the Fourier spectrum. This method works even for high lattice strength where interference peaks disappear in the atomic density distribution.
We theoretically study the loading of a two-species Bose-Einstein condensate to an optical lattice in a tightly-confined one-dimensional trap. Due to quantum fluctuations the relative inter and intra species phase coherence between the atoms and the on-site atom number fluctuations are reduced in the miscible regime. For the immiscible case the fluctuations are enhanced and the atoms form metastable interleaved spatially separated domains where the domain length and its fluctuations are affected by quantum fluctuations.
Monte Carlo method within, so called, classical fields approximation is applied to one dimensional weakly interacting repulsive Bose gas trapped in a harmonic potential. Equilibrium statistical properties of the condensate are calculated within a canonical ensemble. We also calculate experimentally relevant low order correlation functions of the whole gas.
We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different ex…
We investigate nonequilibrium energy transfer in a single-site Bose-Hubbard model coupled to two thermal baths. By including a quantum kinetic equation combined with full counting statistics, we investigate the steady state energy flux and noise power. The influence of the nonlinear Bose-Hubbard interaction on the transfer behaviors is analyzed, and the nonmonotonic features are clearly exhibited. Particularly, in the strong on-site repulsion limit, the results become identical with the nonequilibrium spin-boson model. We also extend the quantum kinetic equation to study the geometric-phase-in…
For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light. The observed agreement of the scale factor with the environment temperature both directly confirms the therm…
An analytic expression is derived for a force on a weak point impurity arising from the scattering of quantum fluctuations in a slow-moving, weakly interacting, three-dimensional Bose-Einstein condensate at zero temperature. In an infinitely extended geometry, this force is shown to exist at any arbitrarily small flow velocity below Landau's critical velocity. Furthermore, this force is shown to be directly proportional to the flow speed.
By using a two-mode description, we show that there exist the multistability, phase transition and associated critical fluctuations in the macroscopic tunneling process between the halves of a double-well trap containing a Bose-Einstein condenstate. The phase transition that two of the triple stable states and a unstable state merge into one stable state or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunneling energy goes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for the phase diffe…
We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c = 1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.
Solutions for the Nonlinear Schrodinger equation for collapsing Bose gas with attraction. This is a copy of the paper published in 1992 in Proceedings of NATO Advanced Research workshop on Singularities in Fluids, Plasmas and Optics (Heraklion, Greece) edited by R.E. Caflisch and G.C. Papanicolaou (Kluwer Academic).
We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.
The condensate number distribution during the transition of a dilute, weakly interacting gas of N=200 bosonic atoms into a Bose-Einstein condensate is modeled within number conserving master equation theory of Bose-Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs-Boltzmann equilibrium.
We consider several models of interacting bosons in a one dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta interaction. The lattice corrections corresponding to the different models are contrasted.
For the recently introduced $μ$-deformed analog of Bose gas model ($μ$-Bose gas model), its thermodynamical aspects e.g. total number of particles and the partition function are certain functions of the parameter $μ$. This basic $μ$-dependence of thermodynamics of the $μ$-Bose gas arises through the so-called $μ$-calculus, an alternative to the known $q$-calculus (Jackson derivative, etc.), so we include main elements of $μ$-calculus. Likewise, virial expansion of EOS and virial coefficients, the internal energy, specific heat and the entropy of $μ$-Bose gas show $μ$-dependence. Herein, we stu…
